To find the constant of proportionality in the relationship given, you can use the formula:
\[ k = \frac{y}{x} \]
where \( k \) is the constant of proportionality, \( y \) is the cost, and \( x \) is the number of bottles manufactured.
Looking at the data in the table, let's calculate \( k \) for one of the points (we can use any point where \( x \) is not zero):
Using the point (25, 20): \[ k = \frac{20}{25} = 0.8 \]
Let's verify this using another point (50, 40): \[ k = \frac{40}{50} = 0.8 \]
And one more point (100, 80): \[ k = \frac{80}{100} = 0.8 \]
In all cases, the value of \( k \) is consistently 0.8.
Therefore, the constant of proportionality is:
A. 0.80